Sets, relations & functions worksheet with answers

Free printable Sets, relations & functions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

Let A = {d, e} and B = {1, 2, 3, 4}. Find |𝒫(𝒫(A))|.

A = {d, e}B = {1, 2, 3, 4}
|𝒫(𝒫(A))| =
2.Easy

How many subsets with exactly 2 elements does A = {1, 2, 3, 4, 5} have? Call the number N.

A = {1, 2, 3, 4, 5}
N =
3.Medium
UABC12345678

Exactly one region of the Venn diagram is the set (C′ ∩ B′) ∩ (A′ ∩ C′). Click its number.

(C′ ∩ B′) ∩ (A′ ∩ C′)
  1. 1region 1
  2. 2region 2
  3. 3region 3
  4. 4region 4
  5. 5region 5
  6. 6region 6
  7. 7region 7
  8. 8region 8
4.Medium
UABC10727101274

Each number in the Venn diagram is the number of elements in that region. Find |(A ∩ B′) ∪ (A ∪ B′)|.

|U| = 59
|(A ∩ B′) ∪ (A ∪ B′)| =
5.Hard
AB123abinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2, 3} and B = {a, b}. Click the description that fits f.

f = {(1, b), (2, b), (3, a)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither
6.Hard
AB1234abcdinjective, not surjectivesurjective, not injectivebijectiveneither

The arrow diagram shows a function f: A → B with A = {1, 2, 3, 4} and B = {a, b, c, d}. Click the description that fits f.

f = {(1, c), (2, a), (3, d), (4, b)}
  1. 1injective, not surjective
  2. 2surjective, not injective
  3. 3bijective
  4. 4neither

Answer key

  1. 1. |𝒫(𝒫(A))| = 16
  2. 2. N = 10
  3. 3. region 7
  4. 4. |(A ∩ B′) ∪ (A ∪ B′)| = 50
  5. 5. surjective, not injective
  6. 6. bijective

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